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We propose a model order reduction framework for incompressible fluid-structure interaction (FSI) problems based on high-order implicit Runge-Kutta (IRK) methods. We consider separate reduced spaces for fluid velocity, fluid pressure and…

Numerical Analysis · Mathematics 2025-12-30 Tommaso Taddei , Xuejun Xu , Lei Zhang

The applicability of the Parareal parallel-in-time integration scheme for the solution of a linear, two-dimensional hyperbolic acoustic-advection system, which is often used as a test case for integration schemes for numerical weather…

Computational Engineering, Finance, and Science · Computer Science 2015-10-09 Daniel Ruprecht , Rolf Krause

In this work, we explore a time-fractional diffusion equation of order $\alpha \in (0,1)$ with a stochastic diffusivity parameter. We focus on efficient estimation of the expected values (considered as an infinite dimensional integral on…

Numerical Analysis · Mathematics 2024-09-04 Josef Dick , Hecong Gao , William McLean , Kassem Mustapha

This paper presents a combined field and boundary integral equation method for solving the time-dependent scattering problem of a thermoelastic body immersed in a compressible, inviscid and homogeneous fluid. The approach here is a…

Numerical Analysis · Mathematics 2018-04-23 George Hsiao , Tonatiuh Sanchez-Vizuet , Francisco-Javier Sayas , Richard Weinacht

We develop a rapid and accurate contour method for the solution of time-fractional PDEs. The method inverts the Laplace transform via an optimised stable quadrature rule, suitable for infinite-dimensional operators, whose error decreases…

Numerical Analysis · Mathematics 2022-02-09 Matthew J. Colbrook , Lorna J. Ayton

A general high-order fully explicit scheme based on projective integration methods is here presented to solve systems of degenerate parabolic equations in general dimensions. The method is based on a BGK approximation of the…

Numerical Analysis · Mathematics 2025-03-10 Tommaso Tenna

We consider the $d=1$ nonlinear Fokker-Planck-like equation with fractional derivatives $\frac{\partial}{\partial t}P(x,t)=D \frac{\partial^{\gamma}}{\partial x^{\gamma}}[P(x,t) ]^{\nu}$. Exact time-dependent solutions are found for $ \nu =…

Statistical Mechanics · Physics 2009-02-06 Mauro Bologna , Constantino Tsallis , Paolo Grigolini

The goal of the present work is to solve a linear dispersive equation with variable coefficient advection on an unbounded domain. In this setting, transparent boundary conditions are vital to allow waves to leave (or even re-enter) the,…

Numerical Analysis · Mathematics 2021-06-09 Lukas Einkemmer , Alexander Ostermann , Mirko Residori

The numerical solution of implicit and stiff differential equations by implicit numerical integrators has been largely investigated and there exist many excellent efficient codes available in the scientific community, as Radau5 (based on a…

Numerical Analysis · Mathematics 2025-06-27 Nicola Guglielmi , Ernst Hairer

We consider the initial/boundary value problem for a diffusion equation involving multiple time-fractional derivatives on a bounded convex polyhedral domain. We analyze a space semidiscrete scheme based on the standard Galerkin finite…

Numerical Analysis · Mathematics 2015-06-18 Bangti Jin , Raytcho Lazarov , Yikan Liu , Zhi Zhou

This paper is concerned with an alternative analytical solution of time-fractional nonlinear Schrodinger equation and nonlinear coupled Schrodinger equation obtained by employing fractional reduced differential transform method. The…

Numerical Analysis · Mathematics 2016-11-23 Brajesh Kumar Singh , Pramod Kumar

In this paper, a fast synthetic iterative scheme is developed to accelerate convergence for the implicit DOM based on the stationary phonon BTE. The key innovative point of the present scheme is the introduction of the macroscopic synthetic…

Computational Physics · Physics 2018-12-18 Chuang Zhang , Songze Chen , Zhaoli Guo , Lei Wu

In this work, we analyze a Crank-Nicolson type time stepping scheme for the subdiffusion equation, which involves a Caputo fractional derivative of order $\alpha\in (0,1)$ in time. It hybridizes the backward Euler convolution quadrature…

Numerical Analysis · Mathematics 2017-02-28 Bangti Jin , Buyang Li , Zhi Zhou

Time-implicit schemes are attractive since they allow numerical time steps that are much larger than those permitted by the Courant-Friedrich-Lewy criterion characterizing time-explicit methods. This advantage comes, however, with a cost:…

Solar and Stellar Astrophysics · Physics 2015-06-16 Maxime Viallet , Isabelle Baraffe , Rolf Walder

This article presents stability and convergence analyses of subgrid multiscale stabilized finite element formulation of non-Newtonian power-law fluid flow model strongly coupled with variable coefficients Advection-Diffusion-Reaction…

Numerical Analysis · Mathematics 2021-02-19 Manisha Chowdhury , B. V. Rathish Kumar

In this work a Feynman-Kac path integral method based on Levy measure has been proposed for solving the Cauchy problems associated with the space-time fractional Schroedinger equations arising in interacting systems in fractional quantum…

Quantum Physics · Physics 2023-06-27 Sumita Datta , Radhika Prosad Datta

The time-fractional diffusion equation is considered, where the time derivative is either of Caputo or Riemann-Liouville type. The solution of a general initial-boundary value problem with time-dependent boundary conditions over bounded and…

Analysis of PDEs · Mathematics 2023-01-04 M. Rodrigo

We present a novel fully implicit hybrid finite volume/finite element method for incompressible flows. Following previous works on semi-implicit hybrid FV/FE schemes, the incompressible Navier-Stokes equations are split into a pressure and…

Numerical Analysis · Mathematics 2023-02-14 Alessia Lucca , Saray Busto , Michael Dumbser

A novel explicit method to model Lorentz linear dispersive media with finite difference method are presented. The method shows an explicit method without any modification to the Leap-Frogging scheme. The polarizations of the Lorentz media…

Numerical Analysis · Mathematics 2020-07-22 Hiroshi Abe

This paper deals with the investigation of the computational solutions of an unified fractional reaction-diffusion equation, which is obtained from the standard diffusion equation by replacing the time derivative of first order by the…

Analysis of PDEs · Mathematics 2012-10-05 R. K. Saxena , A. M. Mathai , H. J. Haubold